# Tag Info

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I'm confused. Are you really going to try to make this sort of distinction when teaching geometric figures to students "around 9-13 years old"? Students that age (and engineers my age -- ...
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### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

One encounters exactly the same issue teaching multivariable calculus when one treats integrals over three-dimensional regions and integrals over the surfaces that are their boundaries. In particular ...
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### Metonymy in mathematics

Metonymy and its relatives, metaphor, polysemy, synecdoche occur all over the place in mathematical writing, and sometimes cause students problems and sometimes don't, because those thought processes ...

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I think the distinction you are raising is not natural to students at this age. I teach undergraduates and graduate students, not elementary schoolers, but I find that it is not natural for ...
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### Can we save the word "unique"?

I don't see this as a major issue, nor do I believe that the word "unique" is in any particular need of saving. There are a large number of terms in mathematics which correspond to ...
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### Uninsulting way to say "this will eventually be easy"

Perhaps not pointing out that the obvious steps are obvious but that the insights are insights. I believe students don't feel bad for not seeing the "magic steps" by themselves, so pointing out that ...

### Can students tell the difference between the "definition if" and the "theorem if"?

Not formal research, but some decades of experience teaching both undergrad and graduate level courses, and "editing" PhD theses and such: It appears that even many serious professional ...
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### Examples of Mathematical Slang

One of the most colorful names I have heard is the Chicken Mc Nugget theorem: for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ ...

### What is it called when terms disappear when reducing fractions?

So German "$b$ kürzt sich weg" becomes in English "$b$ cancels out". We may also say "$b$ is eliminated".
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### Uninsulting way to say "this will eventually be easy"

One thing that you might want to do early on in your course is think about the classroom norms that you wish to establish. From your post, it seems like an example of a norm in your class is that it ...
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### Examples of Mathematical Slang

In Central Mexico, the expression $$x_{\pm} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ that solves quadratic equations of the form $ax^2 + bx + c = 0$ is called "fórmula del ...

### What's the common word for equations and inequalities?

My phrase has always been math "statement". Equations and inequalities clearly assert/state a relationship between two or more things. My go-to direction using this would be something like: &...
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### How to reduce ambiguity in the following question?

The ambiguous answer is relatively correct (actually you need to know how old they are at the start of the problem). But each fission is an individual splitting, not a generation. Perhaps this: A ...
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### Uninsulting way to say "this will eventually be easy"

For presenting proofs, I would only use terminology such as "obviously", "clearly", "routine", etc if it would be for a course just below the class had the student had 'perfect' recollection. For ...
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### Examples of Mathematical Slang

How about the shoelace formula for the area of an arbitrary simple polygon?                     (Image from Wikipedia.) The formula computes the ...
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### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I confess, when you start talking about 1-D triangles, my own first thought is "how can you have non-colinear points in 1-D?". So, I imagine most students that age will have a far more ...
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### Language as a barrier to learn math

Some examples: "One plus five squared" could be read as $(1+5)^2$ or $1+5^2$. This is a well-known ambiguity in natural language, for example in the following sentence I saw a man on a hill with a ...
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### Phrasing the Van Hiele levels in student-friendly language

The argument has been made that this is sort of a misappropriation of the terms, because the levels are meant to define levels of understanding rather than levels of detail. I'm assuming what you're ...

### Can we save the word "unique"?

To my mind the defintion "Every x has a unique f(x)" of one-to-one is problematic because "has a unique" is neither clear English nor precise. The definition is usually stated as "$f(x) = f(y)$ ...
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### How to word this exercise about converting "English" into interval notation?

This is my suggestion. Write each set of numbers in interval notation. (a) All real numbers between 5 and 7, including 5 but not including 7. (b) All real numbers between 1 and 10, including both 1 ...
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### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

Many of the geometric figures are so elementary that they are deeply rooted in daily language, and there seems to be no great solution. I agree with you here, and I think this is the key point. To me ...
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### Examples of Mathematical Slang

My elementary students always wanted to know the name of the symbol shown here: We called it the division house as did many of my colleagues, but my students wanted a mathematical name. We therefore ...
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I am comfortable saying "Solve the equation $x+2$=4" and also saying "Using the equation $(a+b)(a-b)=a^2-b^2$, we see that...". On other other hand I would only ever speak of solving an equation, not ...